1/2(14x+16)-17=-4/5(25x-30)

Solution for 1/2(14x+16)-17=-4/5(25x-30) equation:

1/2(14x+16)-17=-4/5(25x-30)

We move all terms to the left:

1/2(14x+16)-17-(-4/5(25x-30))=0


Domain of the equation: 2(14x+16)!=0

x∈R



Domain of the equation: 5(25x-30))!=0

x∈R


We calculate fractions


(5x2/(2(14x+16)*5(25x-30)))+(-(-8x1)/(2(14x+16)*5(25x-30)))-17=0


We calculate terms in parentheses: +(5x2/(2(14x+16)*5(25x-30))), so:

5x2/(2(14x+16)*5(25x-30))

We multiply all the terms by the denominator


5x2

We add all the numbers together, and all the variables

5x^2

Back to the equation:

+(5x^2)



We calculate terms in parentheses: +(-(-8x1)/(2(14x+16)*5(25x-30))), so:

-(-8x1)/(2(14x+16)*5(25x-30))

We add all the numbers together, and all the variables

-(-8x)/(2(14x+16)*5(25x-30))

We multiply all the terms by the denominator


-(-8x)

We get rid of parentheses

8x

Back to the equation:

+(8x)


a = 5; b = 8; c = -17;
Δ = b2-4ac
Δ = 82-4·5·(-17)
Δ = 404
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{101}}{2*5}=\frac{-8-2\sqrt{101}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{101}}{2*5}=\frac{-8+2\sqrt{101}}{10}
$